Question: Simplify to lowest terms. $\dfrac{60}{40}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 40? $60 = 2\cdot2\cdot3\cdot5$ $40 = 2\cdot2\cdot2\cdot5$ $\mbox{GCD}(60, 40) = 2\cdot2\cdot5 = 20$ $\dfrac{60}{40} = \dfrac{3 \cdot 20}{ 2\cdot 20}$ $\hphantom{\dfrac{60}{40}} = \dfrac{3}{2} \cdot \dfrac{20}{20}$ $\hphantom{\dfrac{60}{40}} = \dfrac{3}{2} \cdot 1$ $\hphantom{\dfrac{60}{40}} = \dfrac{3}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{40}= \dfrac{2\cdot30}{2\cdot20}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot10}= \dfrac{2\cdot 2\cdot 5\cdot3}{2\cdot 2\cdot 5\cdot2}= \dfrac{3}{2}$